Polarization compensated stereoscopic projection

ABSTRACT

Disclosed embodiments include stereoscopic systems having at least one compensator operable to reduce the sensitivity of polarization control over incidence angle of image source optics and analyzer optics. In an exemplary embodiment, the disclosed compensator is operable to compensate polarization changes induced by optics at either or both the image source subsystem and the analyzer subsystem, in which the polarization changes would be operable to cause leakage at the analyzer subsystem if uncompensated. As such, the disclosed compensators and compensation techniques are operable to reduce leakage at the analyzer subsystem even if the disclosed compensator may be located at the analyzer subsystem.

PRIORITY CLAIM

This application is a continuation application of and claims priority toU.S. patent application Ser. No. 13/471,224, entitled “Polarizationcompensated stereoscopic systems”, filed May 14, 2012, which relates andclaims priority to commonly-assigned U.S. Provisional Patent ApplicationNo. 61/485,497, filed May 12, 2011, and entitled “Polarizationcompensated stereoscopic projection,” which is incorporated herein byreference for all purposes.

TECHNICAL FIELD

The present disclosure generally relates to polarization-basedstereoscopic systems, and more particularly, compensatedpolarization-based stereoscopic systems.

BACKGROUND

Stereoscopic systems operate by presenting two distinct images to aviewer, a first image being presented to the right eye and a secondimage being presented to the left eye. Polarization or spectral-divisionmethods may be used to separate the two images. The right-eye andleft-eye images may be coded with orthogonal polarizations at an imagesource, and viewer polarization optics may allow light of orthogonalpolarization states to be passed onto different eyes, thereby creatingthe perception of 3D images.

BRIEF SUMMARY

A first disclosed exemplary embodiment is directed to a stereoscopicimaging system comprising an imager subsystem operable to output lightof first and second states of polarization (SOP) and an analyzersubsystem operable to substantially block light of the first SOP fromtraveling along a first path and to substantially block light of thesecond SOP from traveling along a second path. In an embodiment, theimage source subsystem comprises a first optical element operable tocause a first polarization change on light passing therethrough, and theanalyzer subsystem comprises a second optical element operable to causea second polarization change, and the first and second polarizationchanges, if not compensated, would at least partially cause at least oneof a leakage of light of the first SOP along the first path or a leakageof light of the second SOP along the second path. Either the imagesource subsystem or the analyzer subsystem comprises a compensatorconfigured to at least reduce both the first and second polarizationchanges.

Another exemplary embodiment of the present disclosure is directed to astereoscopic projector system comprising a projection subsystem operableto output light of first and second SOPs, and an analyzer subsystemoperable to substantially block light of the first SOP from travelingalong a first path and to substantially block light of the second SOPfrom traveling along a second path. The projector subsystem comprises afirst optical element operable to cause a first polarization change onlight passing therethrough, and the analyzer subsystem comprises asecond optical element operable to cause a second polarization change,and the first and second polarization changes, if not compensated, wouldat least partially cause at least one of a leakage of light of the firstSOP along the first path or a leakage of light of the second SOP alongthe second path. The projector subsystem comprises a compensatorconfigured to at least reduce both the first and second polarizationchanges.

Yet another exemplary embodiment is directed to a stereoscopic displaysystem comprising an image source subsystem operable to output light offirst and second SOPs. The image source subsystem comprises an LCDpanel, an exit polarizer optically following the LCD panel, and a stripepatterned quarter wave plate (QWP) aligned with the LCD panel. Thestereoscopic display system further comprises an analyzer subsystemoperable to substantially block light of the first SOP from travelingalong a first path and to substantially block light of the second SOPfrom traveling along a second path, the analyzer subsystem comprisinganalyzing quarter wave plates and polarizers each being operable toreceive light from one of the analyzing quarter wave plates. A first+C-plate is either disposed in the image source subsystem between theexit polarizer and the stripe patterned QWP or disposed in the analyzersubsystem optically following one of the analyzing quarter wave plates.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a schematic diagram of an exemplary model of apolarization-based stereoscopic projection system, in accordance withthe present disclosure;

FIG. 2 illustrates a schematic diagram of a “facet model” for a screen,in accordance with the present disclosure;

FIG. 3 illustrates a schematic diagram of an exemplary cinematicarrangement, in accordance with the present disclosure;

FIG. 4 illustrates a chart correlating the retardation as a function offacet incidence angle, in accordance with the present disclosure;

FIG. 5 illustrates a 2D cross-sectional schematic diagram of anexemplary theatre auditorium, in accordance with the present disclosure;

FIG. 6A illustrates a schematic diagram of an uncompensated stereoscopicsystem, in accordance with the present disclosure;

FIG. 6B illustrates a schematic diagram of an uncompensated circularstereoscopic system, in accordance with the present disclosure;

FIG. 7A illustrates a schematic diagram of a first exemplary compensatedstereoscopic system, in accordance with the present disclosure;

FIG. 7B illustrates a schematic diagram of a second exemplarycompensated stereoscopic system, in accordance with the presentdisclosure;

FIG. 8A illustrates a schematic diagram of a first exemplary compensatedcircular stereoscopic system, in accordance with the present disclosure;

FIG. 8B illustrates a schematic diagram of a second exemplarycompensated circular stereoscopic system, in accordance with the presentdisclosure;

FIG. 9 illustrates a schematic diagram of an exemplary model of a cinemaconfiguration in accordance with the present disclosure;

FIG. 10 illustrates a schematic diagram of the exemplary model of thecinema of FIG. 9, with light paths unfolded across a facet plane, inaccordance with the present disclosure;

FIG. 11 illustrates a chart of a comparison of contrast ratios toprojection angles for various minimum PCR value, in accordance with thepresent disclosure;

FIG. 12 illustrates a chart of a comparison of contrast ratios toprojection angles for various minimum PCR value in a circularstereoscopic system, in accordance with the present disc;

FIG. 13 illustrates a schematic side view of a stereoscopic systemconfiguration having vertical offset on the incidence angles, inaccordance with the present disclosure;

FIG. 14 illustrates a schematic diagram of a stereoscopic systemcompensated for vertical offset, in accordance with the presentdisclosure;

FIG. 15 illustrates a schematic diagram of an exemplary film patternedretarder (FPR) system, in accordance with the present disclosure;

FIG. 16A illustrates a polar plot of a luminance state with parallelquarter wave retarders between crossed polarizers and a polar plot of adark state with crossed quarter wave retarders between crossedpolarizers, in accordance with the present disclosure;

FIG. 16B illustrates a polar plot of the contrast ratio for an exemplaryFPR system, in accordance with the present disclosure;

FIG. 17 illustrates a schematic diagram of a first exemplary compensatedFPR stereoscopic system, in accordance with the present disclosure;

FIG. 18 illustrates a schematic diagram of a second exemplarycompensated FPR stereoscopic system, in accordance with the presentdisclosure;

FIG. 19 illustrates a polar plot of the contrast ratio for an exemplarycompensated FPR system, in accordance with the present disclosure;

FIG. 20A illustrates a schematic diagram of an exemplary dual-projectionstereoscopic system, in accordance with the present disclosure; and

FIG. 20B illustrates a schematic diagram of an exemplary compensateddual-projection stereoscopic system, in accordance with the presentdisclosure.

DETAILED DESCRIPTION

FIG. 1 is a schematic diagram illustrating an exemplary model of apolarization-based stereoscopic projection system 100. The performanceof the polarization-based stereoscopic projection system 100 may bedetermined by three elements: 1) polarization optics 102 at theprojector 104; 2) action of the polarization preserving screen 106; and3) polarization optics 108 at the viewer 110. A simplified layout ofthese structures is illustrated in FIG. 1, where the incidence anglerelative to normal, θ, and azimuth angle, φ, may be different on eachstructure.

The viewing experience provided by the system 100 may be compromised bynumerous performance-affecting factors, but compensation through theadjustment and/or addition of polarization optical components to accountfor performance-affecting factors may mitigate or even eliminate thenegative impact on viewing experience. Some metrics used to assessperformance include polarization contrast ratio (PCR) associated with 3Dcross-talk, overall light efficiency, brightness uniformity, overallcolor shift, and color uniformity. PCR is a sensitive indicator ofpolarization fidelity, and is calculated as the ratio of (photopicallyweighted white) power transmitted through a lens to the intended eye, tothat leaking through the lens intended for the other eye.

Exemplary embodiments of the present disclosure are provided toillustrate exemplary approaches that may allow for optimum performance,even when extremely aggressive projection and viewing angles areinvolved. It is to be appreciated that some embodiments of the presentdisclosure may refer to particular illustrated projection or displaysystems, the exemplary compensation approaches disclosed herein may besuitable for improving the performance of any polarization based 3Dsystem, including but not limited to single projector sequential (e.g.,DLP), single projector spatial (e.g., SONY SXRD), dual projector, dualengine systems, and 3D displays, such as film patterned retarder (FPR)systems. In some embodiment, compensation may be accomplished at theprojector or the display to allow for a single compensating structurethat optimizes the experience for the viewing audience. This approachmay allow for the benefit of realizing a relatively sophisticatedcompensation structure without adding significant cost to the system andoperating cost. Embodiments of the present disclosure include cinemasystems, where inexpensive disposable 3D glasses are distributed tocustomers. Some embodiments may include compensation structures at theprojector that can correct deterministic polarization errors that existthroughout the system, including the projector, the screen, the eyewear,and even the geometry of the projection system.

In other embodiments where eyewear cost is not as critical, compensationcan exist at both the projector and viewer to more precisely compensatepolarization errors. Certain portable front-projection systems involvevery short throw-ratio (ratio of screen distance to screen width),multiple broadly distributed viewers, and short viewing distances.Unlike the cinema, a portable projector can be located below allviewers, and can be closer to the screen than any viewers. Without suchcompensation, the quality of the 3D experience may be unacceptable.

According to the present disclosure, compensation configurations mayinvolve adjustment in existing projector polarization optics and/or theaddition of retarder elements. These elements can take many forms,including stretched polymer films, as-cast polymer films with intrinsicbirefringence, liquid crystal cells, cross-linkable liquid crystalpolymers, bulk crystals, and the like. Retarder elements used tocompensate polarization based 3D systems in accordance with thedisclosed principles are generally described in the following terms:

-   -   a. +A-Plate, −A-Plate: These are uniaxial linear retarders with        optic axis in-plane, with positive and negative anisotropy,        respectively.    -   b. +C-Plate, −C-Plate: These are uniaxial linear retarders with        optic axis normal to the plane of the element, with positive and        negative anisotropy, respectively.    -   c. Biaxial Retarder. This may include specific Nz values (ratio        of thickness direction retardation to in-plane retardation) as        needed for a specific compensation requirement.    -   d. O-Plate: In principle this is any retarder that has oblique        orientation of the retarder axes. In many instances this is        accomplished by tipping the retarder to create an asymmetry.

Compensators are generally described in Robinson et al., “PolarizationEngineering for LCD Projection” (July 2005), which is hereinincorporated by reference in its entirety. It is to be appreciated thatany reference to a compensator in the present disclosure may be areference to any of the above described elements for compensation,either acting alone or in any combination thereof, whether directed orindirectly connected. A reference to a compensator in the presentdisclosure may also be a reference to elements for compensation known inthe art but not described herein.

Referring back to FIG. 1, factors that may produce a deterministicpolarization change in the projection system 100 may include

-   -   1. Sensitivity of projector polarization optics (PPO) 102 and        viewer polarization optics (VPO) 108 to incidence angle and        azimuth angle.    -   2. Sensitivity of screen 106 to incidence angle.    -   3. Differential incidence angle between the projection vector        (not shown) and viewing vector (not shown) produced by the        projection screen 106.    -   4. Vertical offset, resulting from height difference between        projector 104 and viewer 110.    -   5. Horizontal offset, resulting from displacement of the viewer        110 from the plane containing the projector 104 and the center        of the screen 106.

These factors can be evaluated via polarization ray tracing, and aredistinguished from random scatter events, such as haze from opticalcomponents, pseudo-depolarization from multiple reflection events fromthe screen 106, or scatter from sub-wavelength structures associatedwith the screen 106. It will be considered here that random scatter isuncorrelated with the above and can be added incoherently to powercalculations, and power ratio calculations such as PCR.

Various elements for the PPO 102 and VPO 108 may be sensitive toincidence angle, including linear polarizers, retardation films, andliquid crystal devices. Even substrates and coatings may induceunintended polarization change. The polarization change may be a shiftin a desired retardation value, an undesired change in the relativepower projected onto the eigen-polarizations (or change in amplitudesplitting) of an anisotropic element, or a shift in the transmissionassociated with eigen-polarizations (e.g., dichroism or diattenuation).Generally, a goal of compensation may be to optimize contrast fornormally incident light, while mitigating the effects of polarizationchange for other angles of incidence. Optimization may be based on alayout of optical components that assumes a common incidence anglethrough the elements, including the encoding optics at the projector andthe decoding optics at the viewer. To the extent that the PPO 102 andVPO 108 track each other in polar angle sensitivity, performance can inprinciple be maintained. Under these circumstances, optimum compensationsolutions for polarization change due to sensitivity of the PPO 102 andVPO 108 above can be determined, as described in the commonly-owned U.S.patent application Ser. No. 13/182,381, which is herein incorporated byreference.

FIG. 2 illustrates a schematic diagram showing a “facet model” for ascreen 200, which may be similar to screen 106 shown in FIG. 1. Asdiscussed above, polarization change may be induced from the reflectionassociated with the projection screen 200. For simplicity, the anglesensitivity of the screen 200 is described here in terms of theillustrated “facet model.” Rays incident on a polarization preservingscreen surface may (ideally) be local specular reflections, as shown inFIG. 2. From the standpoint of preserving polarization, these specularreflections may ideally be single events which redirect a particularprojection ray to a viewer, as shown.

According to the facet model, the local interaction of light with thescreen 200 represents a mirror reflection from a planar surface (e.g.,metallic surface), as illustrated in FIG. 2. The screen surface can beconsidered a statistical distribution of discrete facets 204 depositedon a substrate 202. FIG. 2 shows one of these facets 204, inclined withnormal vector n_(f) forming an angle θ_(S) with respect to the localsubstrate normal n_(s). Light from the projector probes the surface forfacets that redirect the incoming vector KP, to a particular observationdirection, along vector KO. The angle between these vectors is 2θ_(f),where θ_(f) is the facet incidence angle. The plane containing thesevectors is the local plane of incidence.

Like any mirror, the facet 204 has linear eigen-polarizations, such thatthe local P polarization is in the plane of incidence, and the local Spolarization is normal to both P and the facet normal vector. Fresneldescribes the complex reflection of S and P polarizations fromdielectric interfaces, with more specific analysis for reflection frommetals (such as Aluminum) described in, for example, Born and Wolf,Principles of Optics: Electromagnetic Theory of Propagation,Interference and Diffraction of Light (1999), which is incorporated byreference herein. In general, the reflection produces differences inmagnitude, which can be described in terms of a diattenuation. Adifference in phase also occurs (described in more detail in thecommonly-owned U.S. Pat. No. 7,898,734, which is herein incorporated byreference) in general inducing a change in ellipticity. For a barealuminum reflection, it has been shown in U.S. Pat. No. 7,898,734 thatthe retardation associated with a facet is much more significant thandiattenuation for the angles involved.

FIG. 3 is a schematic diagram showing an exemplary cinematic arrangement300. The projection and observation vectors KP and KO define a facetcoordinate system, which defines the facet plane of incidence 302. Thelocal plane of incidence 302 forms an azimuth angle φ relative to thescreen horizontal 304. For the simple geometry shown, the azimuth angleis common to all elements in the system, including the PPO 306, thefacet 308, and the VPO 310. If it is considered that the facet 308behaves primarily as a pure retarder, the fast and slow axes follow theazimuth, and therefore the facet 308 would have the behavior of aC-plate. For an aluminum mirror, the phase delay associated with theP-polarization is in general larger than that for the S-polarization,giving the facet a +C-plate retardation off normal. However, for mostcinema environments these retardation values are small.

FIG. 4 is a chart showing the retardation at 550 nm (green) in nm, as afunction of facet incidence angle from air onto a specular aluminumcoating. As the magnitude of the facet incidence angle increases, thechange in the State of Polarization (SOP) on reflection from the metalsurface tends to become greater, but is quite small for modest angles.

The distinction between the influence that the facet normal and thescreen (substrate) normal have on performance is to be appreciated.Screen coating processes often obey the central limit theorem, givingfacet slope probability distributions that are approximately Gaussianrelative to substrate normal. The facets are typically uniformlydistributed in azimuth, so the diffuser is not directional and issymmetric with respect to the substrate normal. For instance, a typicalsilver screen has a 20° half-power angle, independent of azimuth,meaning that the population density per solid angle of facets inclinedat 10° to the substrate normal is approximately half of that in theplane of the substrate.

Referring back to FIG. 2, when the projection and observation vectors KPand KO are not symmetrically placed with respect to the substrate normaln_(s), the facet normal n_(f) has a tilted orientation, θ_(S). In a caseof symmetrically increasing incidence/observation angles (θ_(F)), withfixed facet angle normal to the substrate (θ_(S)=0), the same (in-plane)population of facets 204 is involved in the scattering event regardlessof angle. So to the extent that large angles do not result in shadowingor multiple scattering events, polarization change may be largelydetermined by Fresnel effects that increase with facet incidence angle,θ_(F). Brightness may remain fairly constant for a modest range inangles. Conversely, in a case in which projection and observationdirections KP and KO are counter-propagating (retro-reflected), as thefacet angle (θ_(S)) increases, the facet incidence angle (θ_(F)) mayremain zero, but the population of facets 204 involved in the scatteringevent is constantly changing. The population density of facets 204 fallswith θ_(S) (with resulting loss in brightness), but there are in generalno Fresnel polarization shifts. The facet angle is highly relevant tothe statistical probability of reflection, and thus observed brightness.But indirectly, it can also determine PCR, since leakage (thedenominator term) is frequently “white” in angle space, while the imagebrightness (the numerator term) tends to follow the gain curve.

An aspect of the present disclosure pertains to the optimization ofpolarization control for a variety of PPO, VPO, and projection andviewing geometries. In some embodiments, performance optimization may bebased on some assumptions about the projection and viewing environment.Since environments are not standardized, even in the context of digitalcinema, a single compensation solution cannot be optimum for thefront-projection ensemble. But specifically in a cinema environment,there is a set of reasonable assumptions that may be applied, either inpart or in whole, for optimization design:

-   -   1. The projector is centered horizontally with respect to the        screen.    -   2. The projector is in a vertical position that is in general        higher than any viewing location. In a cinema environment, the        projector is typically higher than the screen center, and can        even be located at/above the top of the screen.    -   3. The vector normal to the PPO is pointed at the screen center.        This may be done to ensure that the highest performance is        measured at screen center, ideally falling symmetrically (and        gradually) as the angle increases. This assumption is based on        the likely scenario that performance of the PPO is typically        optimum at normal incidence.    -   4. Performance may be theoretically optimized for a single        location in observation space, known as the “ideal viewer” (IV).        In general, the location of the IV is constrained to be centered        horizontally. The assumption again may be that performance of a        passively compensated system will fall equally for viewers        equidistant and on either side of the IV. The IV is also        constrained in space by the particular auditorium geometry. In        order for a single compensation scheme to be effective in        virtually any theatre auditorium, the IV may further incorporate        statistical analysis of theatre geometries, including, e.g.,        ensemble average viewer height and distance from the screen (as        a percent of throw distance).    -   5. In an embodiment, selection of the IV can further incorporate        nonlinearity in the functional decay in performance for        observers within a particular radius of the IV. This can be        useful for maximizing the quality of the experience for as large        a population surrounding the IV as possible. A performance        “Q-factor” can be assessed for each viewing location, with the        IV associated with the center of mass. Conversely, in an        embodiment, some weighting to the selection of the IV can also        be given to achieving a just-acceptable-experience for viewers        in extreme locations of the viewing space. In other words,        optimization may not allow any “seat kills” associated with an        unacceptable viewing experience.    -   6. In an embodiment, passive compensation may not optimize for        general viewing direction, and it may be done for the specific        case in which the viewer gazes at the screen center. In other        words, the vector normal to the VPO is pointed at the center of        the screen. As such, the IV assesses performance with greatest        resolution/sensitivity based on a zone centered on the screen,        with the perception of loss in performance based on observing        other portions of the screen in the periphery (i.e., without        head movement). In an embodiment, performance could also be        optimized for situations where the viewer turns to look directly        at features on the screen, which may be useful for applications        that represent information to viewers, such as, medical imaging,        aviation cockpit displays, etc.    -   7. Embodiments may correct global polarization issues by        compensating at the projector. That is, a compensation stack        placed at the projector can optimize the experience for the IV        by correcting the polarization associated with the deterministic        polarization factors (e.g., Factors 1 through 4) listed above.        In so doing, the eyewear need not be modified to optimize        performance, thus minimizing overall cost. Moreover, certain        compensation materials and configurations may not be practical        for roll-to-roll, or other commodity manufacturing processes.    -   8. Embodiments may include screen curvature, typically a        curvature of the screen about the vertical, ideally with radius        of curvature equal to the throw distance (z).

In some embodiments, compensation for horizontal offset (i.e.,displacement of viewer location from the plane containing the projectorand screen center) may be configured in a symmetric fashion. Forinstance, it may not be beneficial to improve the experience for viewersto the left of center, if it is at the expense of those to the right ofcenter. Accordingly, compensation for horizontal offset may be achievedusing elements that possess the symmetry to improve the experience bothto the left and right of center. The details depend upon the details ofthe projection and eyewear polarization optics.

FIG. 5 is a schematic diagram illustrating a simplified 2D cross sectionof an exemplary theatre auditorium 500, in which the plane of thediagram includes the projector 502 and screen center 504. While it is anunlikely front projection arrangement for the projector 502 and theviewer 506 to be co-located, it is useful for illustrative purposes. Dueto the co-location of the projector 502 and the viewer 506, the normalvectors (not shown) of the PPO 508 and the VPO 510 do not have anyvertical offset. For an arbitrary projection vector, the light probesthe screen surface 514 for facets (not shown) that produce aretro-reflected ray. As such, light is in general normally incident onevery facet that is operable to provide light to the viewer 506, and thescreen 512 therefore has no impact on the SOP. This arrangement isequivalent to reflecting the projector location about the facet plane,as shown in FIG. 5. In this unfolded arrangement, the azimuth angle andincidence angle θ through the PPO 508 are equivalent to that through theVPO 510, thus eliminating issues associated with differential incidenceangle between the projection vector and viewing vector. In effect, thecompensation configuration for the geometry in theatre 500 may bedesigned by considering the VPO 510 and PPO 508 as a single stack andminimizing the impact of incidence angle on overall performance metrics,as outlined above in accordance with the principles of the presentdisclosure. Such compensation schemes are described in thecommonly-owned U.S. patent application Ser. No. 13/010,755, which isincorporated by reference herein.

The following examples are based on optimization for co-location ofprojector and viewer for 3D systems of the present disclosure.

Example 1A

FIG. 6A is a schematic diagram showing a stereoscopic system 600. FIG.6B is a schematic diagram showing a circular polarization stereoscopicsystem 605, which will be described in greater details below. Thestereoscopic system 600 may include an image source subsystem 610operable to output light of first and second states of polarization(e.g., S- and P-polarization) and an analyzer subsystem 620. Theanalyzer subsystem 620 may include eyewear operable to substantiallyblock light of the first state of polarization from traveling along afirst path (e.g., light path to a first eye) and to substantially blocklight of the second state of polarization from traveling along a secondpath (e.g., light path to a second eye). In an embodiment, the imagesource subsystem 610 may include a first optical element operable tocause a first polarization change on light passing therethrough, and theanalyzer subsystem 620 may include a second optical element operable tocause a second polarization change, in which the first and secondpolarization changes, if not compensated, would cause at least one of aleakage of light of the first SOP along the first path or a leakage oflight of the second SOP along the second path.

For example, the PPO 610 and VPO 620 may each include a polarizer 625comprising a functional PVA polarizer film 630 laminated betweentriacetate cellulose (TAC) films 632, 634, 625. In an embodiment, thepolarizer films 630 of PPO 610 and VPO 620 may be substantiallyidentical, and the polarizer orientation and polarizing efficiency maythus be considered ideal. But TAC films 632, 634 may not be isotropicand may behave as a −C-Plate, which may be understood to be a negativeuniaxial retarder with optic axis oriented normal to the film. In theφ=±45° azimuth, this retardation has the greatest impact, furtherdegrading the PCR. Assuming a retardation of −50 nm of −C-plateretardation for each substrate (combined −100 nm), the contrast in theφ=±45° azimuth degrades to 100:1 at 33°, and 50:1 at 40°. Further, at anangle of 75°, the contrast is only 10:1.

FIG. 7A is a schematic diagram showing an exemplary embodiment of acompensated stereoscopic system 700, in accordance with the disclosedprinciples. The compensated stereoscopic system 700 may include an imagesource subsystem 710 operable to output light of first and second statesof polarization (e.g., S- and P-polarization) and an analyzer subsystem720. The analyzer subsystem 720 may include eyewear operable tosubstantially block light of the first state of polarization fromtraveling along a first path (e.g., light path to a first eye) and tosubstantially block light of the second state of polarization fromtraveling along a second path (e.g., light path to a second eye). Likethe image source subsystem 610 and analyzer subsystem 620, in anembodiment, the image source subsystem 710 may include a first opticalelement operable to cause a first polarization change on light passingtherethrough, and the analyzer subsystem 720 may include a secondoptical element operable to cause a second polarization change, in whichthe first and second polarization changes, if not compensated, wouldcause at least one of a leakage of light of the first SOP along thefirst path or a leakage of light of the second SOP along the secondpath. In the illustrated embodiment, the first and second opticalelements may each include a polarizer 725 similar to polarizers 625 inFIGS. 6A & 6B and includes a PVA polarizer film 730 laminated betweenTAC films 732, 734. It is to be appreciated that while the external TAC734 are shown, they have little to no impact on the SOP. To compensatefor the first and second polarization changes induced by the polarizers725 of the image source subsystem 710 and the analyzer subsystem 720, acompensator 740 may be included in the stereoscopic system 700. Thecompensator 740 may be disposed in either the image source subsystem 710or the analyzer subsystem 720, and may be configured to at least reduceboth the first and second polarization changes.

In FIG. 7A, the image source subsystem 710 includes the compensator 740,which may include a biaxial half-wave retarder 742 orientedparallel/perpendicular to the absorption axis, with Nz=0.5. An aspect ofthe biaxiality is that the optic axis remains stable in the 45° azimuthwhen illuminated off-normal. Conversely, the polarizer absorption axesare counter-rotating in this azimuth. As such, the biaxial half-waveretarder optimally reflects the SOP of the input polarization about anoptic axis, correctly orienting it along the analyzer absorption axis.Using a zero-order half-wave retarder in the green, the photopicpolarization contrast remains above 1,000:1 for incidence angles above60°. By placing the compensator 740 in the imaging source subsystem 710,the compensator 740 is operable to substantially compensate for contrastloss experienced by all viewers.

Example 1B

FIG. 7B illustrates an embodiment of a compensated stereoscopic system705, also in accordance with the disclosed principles. The stereoscopicsystem 705 is similar to stereoscopic system 700 except the stereoscopicsystem 705 includes a compensator 750 instead of the compensator 740. Inan embodiment, the compensator 750 includes an A-plate 752 and C-plate754 as an alternative to the biaxial retarder 742 in the compensator740. The A-plate 752 may be a positive A-plate with 80 nm of retardationand have its slow-axis crossed with respect to the absorption axis ofthe polarizer 730. The A-plate 752 may be followed by a positive C-plate754 with a retardation of 150 nm. The action of this combination may besufficient to compensate both for the retardation of the TAC layers 732and the geometrical rotation of the crossed polarizers 730. Using thiscompensation configuration, the PCR may remain above 660:1 for incidenceangles above 75°.

Example 2A

FIG. 6B is a schematic diagram showing a stereoscopic system 605, whichis similar to stereoscopic system 600 except the image source subsystem610 and the analyzer subsystem 620 of the stereoscopic system 605 eachinclude a quarter-wave retarder 660. The quarter-wave retarder 660allows for a circular polarization based 3D system, which is very commontoday. In the off-state, the quarter-wave retarder 660 of the imagesource subsystem 610 is crossed with the quarter wave retarder 660 ofthe analyzer subsystem 620. The crossed quarter-wave retarders 660,which may be considered as crossed +A-plates, behave similarly to−C-plates in the φ=45° azimuth, thereby adding additional retardationthat further degrades contrast. An uncompensated circular-polarizersystem similar to stereoscopic system 605, which includes TAC layers632, may have a contrast of 100:1 at an incidence angle of 23°. Thecontrast may fall to 50:1 at 27°. Further, at an angle of 75°, thecontrast may be less than 3:1.

FIG. 8A is a schematic diagram showing an exemplary embodiment of acompensated circular stereoscopic system 800. The compensated circularstereoscopic system 800 may include an image source subsystem 810operable to output light of first and second states of polarization(e.g., S- and P-polarization) and an analyzer subsystem 820. In theillustrated embodiment, the image source subsystem 810 and the analyzersubsystem 820 may each include a polarizer 825 having a PVA polarizerfilm 830 laminated between TAC films 832, 834. The image sourcesubsystem 810 and the analyzer subsystem 820 may also includequarter-wave retarders 860, 865, respectively. To compensate for thepolarization changes induced by the quarter-wave retarders 860, 865 andpolarizers 825 of the image source subsystem 810 and the analyzersubsystem 820, a compensator 840 may be included in the circularstereoscopic system 800. The compensator 840 may be disposed in eitherthe image source subsystem 810 or the analyzer subsystem 820. In theillustrated embodiment, the compensator 840 is disposed in the imagesource subsystem 810 following optically the polarizer 825. Asillustrated, the compensator 840 may include a TAC compensator 843followed by a biaxial half-wave retarder 844. In order to compensate forthe crossed +A-plates (i.e., the quarter wave retarders 860, 865) andthe polarizer 825 at the analyzer subsystem 820, the compensator 840further includes +C-plates 844 sandwiching the quarter-wave retarder860. By increasing the +C-plate retardation (e.g., from 50 to 92 nm inthe illustrated embodiment), the contrast of the system may bemaintained above 1,000:1 for angles exceeding 60°.

Example 2B

FIG. 8B illustrates another embodiment of a compensated circularpolarization stereoscopic system 805, in accordance with the disclosedprinciples. The circular polarization stereoscopic system 805 is similarto the circular polarization stereoscopic system 800, except thestereoscopic system 805 includes a compensator 850 instead of thecompensator 840. In an embodiment, the compensator 850 includes anA-plate 852 and C-plate 854 as an alternative to the biaxial retarder842 in the compensator 840. The A-plate 852 may be a positive A-platewith 80 nm of retardation and have its slow-axis crossed with respect tothe absorption axis of the polarizer 830. The A-plate 852 may befollowed by a positive C-plate 854 with a retardation of 200 nm. Tofurther improve contrast, a second positive C-plate 854 with aretardation of 80 nm is added after the quarter-wave retarder (+A-plate)860. The action of this combination may be sufficient to compensate bothfor the retardation of the TAC layers 832, the retardation of thecrossed quarter wave retarders 860, 865, and the geometrical rotation ofthe crossed polarizers 830. Using this compensation configuration, thePCR may remain above 1000:1 for incidence angles above 75°.

The above examples include optimized exemplary embodiments formaximizing contrast over the full field of view to large angles.However, it is to be appreciated that portions of the disclosedcompensators 740, 750, 840, and 850 can be used to enhance performancerelative to uncompensated systems 600 and 605. For instance, the exit+C-plate retarder 744, 754, 844, and 854 used in the above example maybe omitted while still yielding performance that is substantially betterthan an uncompensated system.

In many eyewear lens constructions, there are additional retarders, orretarders that do not possess ideal anisotropy, and improved performancemay be achieved with adjustment in compensation. Two examples of thisare provided here to illustrate the application of the principles of thepresent disclosure.

In an embodiment, low-cost cinema eyewear may contain flat die-cutlenses having the elements of the analyzer subsystem 620 as shown inFIGS. 6A & 6B. While the polarization performance of such a lens can benearly ideal, the optical properties can be quite poor (e.g.,transmitted wavefront distortion, and in particular irregularity). Forcircular polarization eyewear, a linear polarizer is laminated to aquarter-wave retarder using a pressure-sensitive adhesive, furtherexacerbating the problem. In an exemplary embodiment, to counteractthis, polarizing sunglass lens fabrication techniques can be applied.Techniques such as insert-molding, injection molding on the lensback-side, thermo-forming incorporating press-polishing, andthermoforming stack-ups involving additional substrates (e.g., acrylic)may be used to improve mechanical support and optical quality. However,such processes may compromise polarization control, including theuniformity of polarization control. An addition of foreign materialswith mechanical properties that are not matched, stresses fromadhesives, and stresses from pressure/heat of forming processes tend tonegatively affect polarization properties. In cases where themanufacturing process results in a deterministic effect, compensatorsconfigured according to the principles of the present disclosure may beincorporated into the eyewear to improve the situation.

In some embodiments, in higher optical quality 3D eyewear, the retardermaterial used for the circular polarizer may be selected forformability, but it may not be ideal from a polarization controlstandpoint. Lenses may include retardation film with high intrinsicretardation, or retardation resulting from biaxial stretching. Examplesinclude cellulose acetate propionate (CAP), and cellulose diacetate(DAC), and stretched films with engineered biaxiality. CAP and DAC, likeTAC, possess negative intrinsic (C-plate) retardation, but to a muchlarger degree. A typical DAC/CAP quarter-wave retarder may have 200 nm(or more) of −C-plate retardation. To the extent that the eyewearretardation is consistent, compensators designed according to theprinciples of the present disclosure may be incorporated in the imagingsource subsystem to effectively reduce the intrinsic retardation of CAPand DAC for all viewers. For instance, the retardation of the +C-plateretarder 854 of FIG. 8B may be increased appropriately to compensate forany negative intrinsic retardation associated with the analyzing thequarter wave.

Similar polarization control degradation may exist if a substrate islaminated external to a uniaxial quarter-wave retarder. If a substrateis required to provide mechanical support or improve opticalcharacteristics, it ideally may be isotropic. However, there are fewsubstrates that may be manufactured with low in-plane retardation(ideally <3 nm) and be thermoformable without introducing in-planeretardation. TAC is one such substrate, but depending on the designthickness, it may introduce significant additional C-plate retardation.As discussed above, such retardation may be compensated by a suitableadjustment in retardation values of the compensator at the projector oreyewear.

FIG. 9 illustrates a configuration 900 more representative of thetypical cinema configuration. FIG. 10 illustrates a configuration 1000having an unfolded optical path, based on reflection of the projector1010 about the facet plane in the configuration 900 shown in FIG. 9. Asdescribed in the above discussed '381 patent application, furtheradjustment in compensation may be made to account for differencesbetween projector and observer incidence angles. In the embodimentillustrated in FIG. 9, the viewer is moved toward the screen along thenormal direction, with a center-screen viewing distance, L. In thiscase, the screen has the effect of decoupling the projection angles fromthe viewing angles, such that the projector and observer incidenceangles may be determined according to equation (1):

$\begin{matrix}{\theta_{O} = {\tan^{- 1}\left\lbrack {\frac{Z}{L}\tan\;\theta_{P}} \right\rbrack}} & (1)\end{matrix}$Also, the facet incidence angle is in general no longer zero and isrelated to the projector and observer angles by equation (2):

$\begin{matrix}{{\theta P} = \left\lbrack \frac{\theta_{O} - \theta_{P}}{2} \right\rbrack} & (2)\end{matrix}$Due to the symmetry of the arrangement, the above relationships areindependent of azimuth.

In an embodiment, an observer may be positioned midway between theprojector 1010 and screen 1020. In such an embodiment, according toequations 1 and 2, if the maximum projection angle is 20°, the maximumviewing angle is 36°, and the maximum facet angle is 8°. In a morechallenging scenario, if the maximum projection angle is 30°, themaximum viewing angle is 49°, and the maximum facet angle is 9.6°. Thisexample shows that the observer angles are by far steeper, while theFresnel contribution to polarization change is relatively small due tothe small facet angles. As FIG. 2 shows, the retardation associated withthe facet at 10° is approximately 1 nm, allowing it to be disregardedfrom the compensation scheme in some embodiments.

Because the angles through the VPO are in general larger than thosethrough the PPO, the contribution to polarization error is magnified. Itis desirable in some embodiments to accomplish all compensation at theprojector, but because the angles are smaller, adjustments may be madeto optimally compensate for the angle differential. Specific exemplaryembodiments of PPO/VPO optics configurations according to the presentdisclosure are provided below.

The exemplary embodiments in FIGS. 7A, 7B, 8A, and 8B were analyzedusing rigorous 4×4 Berreman matrix methods, which included both theeffect of geometrical rotation of elements such as the polarizers, aswell as retardation shift, under the condition of a common incidenceangle. For the following embodiments, a simplified analysis is done thatexamines the effect of retardation shift in isolation. The analysis isperformed in the worst-case azimuth of φ=±45° assuming the relationshipbetween the VPO and PPO angles given above. In some sense, these issuesare separable, in that the geometrical correction from the biaxialhalf-wave retarder and its equivalents (e.g., combination of +A-plateand +C-plate) is independent of the correction for retardation error.Geometrical errors in the optic axis orientation (e.g., for a circularpolarizer based system) do not exist in the φ=±45° azimuth.

Example 3

Turning back to FIG. 7A, in an embodiment, the compensator 740 mayinclude+C-plates 744 sandwiching the retarder 742 to compensate for thepolarization changes of both polarizers 725 and optimize contrast. Thenet retardation of the system is given by equation (3):

$\begin{matrix}{\Gamma_{NET} = {{\Gamma_{TAC}\left( {\theta_{F},{{\pm 45}{^\circ}}} \right)} + {\Gamma_{CONF}\left( {\theta_{F},{{\pm 45}{^\circ}}} \right)} + {\Gamma_{TAC}\left( {\theta_{0},{{\pm 45}{^\circ}}} \right)}}} & (3)\end{matrix}$

In a prior discussed embodiment, the objective may be to minimize theretardation for the IV, while insuring that it is within an acceptablerange for the extreme cases. The optimization for this embodimentfocuses on the extreme projection angles, which for a 1.0 throw ratiomay be roughly θ_(P)=30°. The compensation may be selected so as tomaximize contrast at the extreme angle, while insuring that it does notdip below that value for smaller projection angles.

The retardation of a C-plate, which is independent of azimuth angle, maybe given by equation (4):Γ_(c)(θ,φ)=kn _(o) d[√(1−(sin θ/n _(e))²)−√(1−(sin θ/n _(o))²)]  (4)In equation (4), n_(o) and n_(e) are the ordinary and extraordinaryindices of refraction, respectively, k is the vacuum wave number(k=2π/λ, where λ is the vacuum wavelength), d is the retarder thickness,and θ is the angle of incidence in air. For TAC, indices of 1.47 and1.46 are used respectively for n_(o) and n_(e) for modeling purposes,where k(n_(e)−n_(o))d=−50 nm.

FIG. 11 illustrates contrast ratios over a full range of projectionangles for various minimum PCR value. With a net −100 nm of TACretardation between the PVA polarizers, and no compensation, thecontrast is generally low, and falls monotonically as the viewer movestoward the screen. For example, the PCR is 57:1 for a viewer located atthe 50% point (mid-way between projector and screen). If a +C-plate isadded at the projector, according to the present disclosure, tocompensate both TAC layers, with a retardation matched to the net−C-plate retardation (+100 nm), the system may be substantially fullycompensated for viewing at 100% of the throw distance. For this example,when the index values of n_(o)=1.52 and n_(e)=1.53 are used for thecompensator, the contrast is considerably better, but again fallsmonotonically as the viewer approaches the screen. For example, the PCRis a much improved 246:1 at the 50% viewing point under thiscompensation scheme.

When the +C-plate retardation value is increased according to thepresent disclosure to optimize the contrast for a particular IVdistance, contrasts increase significantly. For example, FIG. 11 showsthat if the IV is selected to be at the 50% viewing distance, theworst-case contrast can be maintained above 300:1 for viewers from below30%, to those at 90%. The compensator retardation value desired at theprojector is roughly twice that of the TAC retardation, in order toovercome the angle difference.

It is noteworthy that the peak PCR attainable decreases when the IV ismoved closer to the screen. There is a relatively significant increasein PCR for all viewing angles when a compensator is added that matchesthe TAC base retardation. But beyond that, the effectiveness ofincreased retardation for viewers very near the screen is limited. Atthe extreme 10% viewing distance, the difference between PCR forcompensation optimized for the IV at 40% is not substantially betterthan that optimized for the IV at 90%. Given that there is a moregradual fall in PCR for viewers behind the IV, optimization based onmaximizing the PCR improvement for all viewers may involve locating theIV to be at about approximately the 50% point.

Example 4

This example is identical to Example 3, except that crossed (+A-plate)quarter wave retarders are inserted between the linear polarizers,oriented at ±45°, representative of a circular-polarization basedsystem, similar to the circular stereoscopic systems 800 or 805discussed above. The net retardation after the addition of theseretarders may be determined using equation (5):Γ_(NET)=Γ_(TAC)(θ_(P),±45°)+Γ_(QW)(θ_(P),±45°)+Γ_(COMP)(θ_(P),±45°)+Γ_(QW)(θ_(O),±45°)+Γ_(TAC)(θ_(O),±45°)  (5)The retardation of an +A-plate retarder is given by equation (6):

$\begin{matrix}{{\Gamma_{QW}\left( {\theta,\varphi} \right)} = {{kd}\left\lbrack {{n_{e}\left. \sqrt{}\left( {1 - \left( {\sin\;{\theta/\left( {n_{e}(\varphi)} \right)^{2}}} \right) - {n_{o}\left. \sqrt{}\left( {1 - \left( {\sin\;{\theta/n_{o}}} \right)^{2}} \right) \right.}} \right\rbrack \right.{where}},{{1/{n_{e}^{2}(\varphi)}} = {\left\lbrack {{\cos^{2}(\varphi)}/n_{e}^{2}} \right\rbrack + \left\lbrack {{\sin^{2}(\varphi)}/n_{0}^{2}} \right\rbrack}}} \right.}} & (6)\end{matrix}$

The above is given in the rotated coordinate system associated with theretarder, where φ=φ−45°. As before, the present analysis is performed atthe net retardation in the (worst-case) φ−±45° azimuth. Relative to theprevious linear polarizer case, the additional retardation associatedwith the crossed quarter-wave retarders is given by equation (7):Γ_(QWNET)(θ,45°)=kd[n _(e)√(1−((sin θ_(P))/n _(o))²)−n _(o)√(1−((sinθ_(P))/n _(o))²)−n _(e)√(1−((sin θ_(O))/n _(e))²)+n _(o)√(1−((sinθ_(O))/n _(o))²)]  (7)

In the case where the IV is located at the projector, this retardationis determined by equation (8):Γ_(CAP) =kn _(e) d[√(1−(sin θ/n _(e))²)−√(1−(sin θ/n _(o))²)  (8)This shows that the retardation of crossed +A-plates in the φ=±45°azimuth has the same functional form as the above −C-plate retarder,with Z-retardation given by the in-plane retardation of a singleA-plate. As such, quarter-wave retarders add additional −C-plateretardation, which may use further compensation accomplished at theprojector in some embodiments.

FIG. 12 shows contrast ratios over a full range of projection angles forvarious minimum PCR value in a circular polarizer system. The parametersare the same as for Example 3, with the quarter-wave parameters given byn_(o)=1.52 and n_(e)=1.53. The quarter wave thickness (d) is selected togive a retardation of 129 nm at a wavelength of 516 nm. To compensatefor the 100% viewing distance (common projection and viewing angles), a+C-plate with 229 nm of retardation may thus be used. This substantiallyimproves PCR. But as before, additional compensation improves the PCR asthe viewer is moved further toward the screen.

In general, the peak contrast attainable with the circular system whenoptimized for a particular IV location is lower than that possible withthe linear case. For example, a system optimized for the IV at 50%maintains a contrast about approximately 60:1 from the 30% viewingposition to the 90% viewing position. As before, the retardation used atthe projector increases as the IV moves closer to the screen; so asystem optimized for 50% has a retardation that is nearly twice that for100% viewing.

Cinema auditoriums typically have other geometrical factors that caninfluence polarization maintenance. This includes screen curvature,vertical offset of projector and vertical offset of viewing. Thesefactors can be reduced to incidence angle and azimuth angles for thethree components that define system performance, as shown in FIG. 1.

Screens may be curved in a cylinder about the vertical, with a radius ofcurvature matched to the throw distance. At the projector height, thethrow distance is constant in the horizontal, and the substrate normalvector coincides with the projection vector. This means that deviationbetween projection and screen normal only occurs in the verticaldirection, which may suppress brightness nonuniformity. In principle, ascreen can have compound curvature, which can match projection andscreen normal vectors for all positions, but this concept has neverenjoyed much popularity.

A flat screen can be compared to a curved screen with identical chordwidth, W. For a projector centered on the screen, the maximum projectionangle may be determined by equation (9):

$\begin{matrix}{{\tan\;\theta_{P}} = \frac{\sqrt{1 + \left( \frac{H}{W} \right)^{2}}}{2\; T}} & (9)\end{matrix}$In equation (9), H is the screen height, W is the screen width, and T isthe throw ratio. Because the throw distance grows with angle off screennormal, the projection angle is diminished. So a throw ratio of T=1, anda screen aspect ratio of W/H=2 gives a maximum projection angle of 29°.

A curved screen has maximum projection angle that may be determined byequation (10):

$\begin{matrix}{{\sin\;\theta_{P}} = \sqrt{\frac{1 + \left( \frac{W}{H} \right)^{2}}{1 + \left( \frac{22}{H} \right)^{2}}}} & (10)\end{matrix}$For the above conditions, equation (10) yields a larger 33° maximumprojection angle.

FIG. 13 is a side view of a projection configuration 1300 havingvertical offset on the incidence angles. Vertical offset may createasymmetry/directionality in the polarization map. The projector verticaloffset in a cinema may be a significant fraction of a half-screen, andat times the projector 1302 may be above the top of the screen 1304. Theheight of the viewer 1306 relative to screen center may be a function ofdistance from the screen 1304, in accordance with the slope of thestadium seating configuration in some embodiments.

FIG. 14 is a schematic diagram illustrating a stereoscopic system 1400compensated for vertical offset in accordance with the disclosedprinciples. The virtual projector location is shown in FIG. 14 for thecenter and upper extreme ray to illustrate the unfolded geometry.Provided that the PPO and VPO normal vectors are oriented at screencenter, and the effect of the facet on the SOP may be ignored, thecontrast is identical to previous examples in which there is no verticaloffset.

Also shown in FIG. 14 is the asymmetry in extreme angles caused by theoffset. The vertical displacement between projector 1402 and viewer 1406increases the projection and facet angles at the top of the screen 1404,and diminishes them at the bottom. Overall, there may be a facet“bias-angle” due to vertical offset. Recalling that the facet may behaveas a +C-plate at screen center, the principle coordinates of theretarder are in-plane and normal to the figure. Any significant non-zeropolarization shift can in principle be compensated according to thepresent disclosure. A planar compensator 1410 having the associatedasymmetry may substantially eliminate facet retardation at all angles.In an embodiment, the compensator 1410 may comprise an O-plate(oblique), which may be implemented by appropriately tilting a C-plateor A-plate. FIG. 14 illustrates this, where tipping the C-platecompensator 1410 forward reduces the incidence angle for rays directedto the bottom of the screen 1404 (thus reducing compensation), andincreases the incidence angle for rays directed to the top of the screen1404 (thus increasing compensation). The retardation and tilt-angle arelikely selected to eliminate facet retardation at screen center.

Though not optimum, compensation can also be accomplished using otherschemes. For instance, in an embodiment, the in-plane retardation may bereduced using a crossed A-plate, which under-compensates the top of thescreen and over-compensates the bottom. To the extent that compensationcan be accomplished by appropriate tilting of portions or all of theexisting PPO structure, and/or adjustment to the retardation of anexisting component, there is no need for an additional compensator.

It is to be appreciated that although some embodiments and examples ofthe present disclosure may refer to particular illustrated projection ordisplay systems, the exemplary compensation approaches disclosed hereinmay be suitable for improving the performance of any polarization based3D system, including but not limited to single projector sequential(e.g., DLP), single projector spatial (e.g., SONY SXRD), dual projector,dual engine systems, and 3D displays, such as film patterned retarder(FPR) systems.

FIG. 15 is a schematic diagram showing an exemplary FPR system 1500.Some advantages of 3D displays based on FPR may include:

1. Low production cost;

2. Low cost eyewear;

3. Comfort due to light weight of passive eyewear used with FPR systems

4. Less orientation dependent; and

5. Flicker elimination.

As shown in FIG. 15, the FPR 3D system 1500 may include stripe patternedquarter wave plate (QWP) 1504, which may be made of liquid crystalpolymer (LCP). The stripe patterned QWP 1504 may be aligned with LCDpixel stripes in the LCD panel 1502 in the horizontal direction. Animage 1510 may be alternately displayed on these horizontal stripes 1502as 3D left and right signals. The exiting light will be converted toleft hand and right hand circular polarized light by the stripepatterned QWP 1504. The eyewear 1506 comprising left and right circularpolarizer (CP) is operable to separate left image from right image, orvise versa, to allow a user 1516 to perceive a 3D image.

In an embodiment, the field of view (FOV) of a display may be a criticaldesign factor. In an embodiment of the system 1500, the striped QWP 1504and the QWP in the eyewear 1506 may both be made of uniaxial a-platematerial (i.e., nx>=ny=nz). Even if they are made of the identicalmaterial for dispersion matching, the system 1500 may still have anarrow field of view (FOV).

FIG. 16 is a polar plot of the contrast ratio of an FPR system similarto the FPR system 1500 of FIG. 15. The narrow field of view is indicatedby the low contrast ratio at about 15:1 in the 45/135 degree azimuthalplane at 40 degree viewing angle, while the contrast ratio is muchhigher at smaller viewing angles.

FIG. 17 is a schematic diagram of a compensated FPR system 1700, inaccordance with the disclosed principles. The FPR 3D system 1700 mayinclude an image source subsystem 1750 comprising an LCD panel 1705,optically followed by an exit polarizer 1710, and a stripe patternedquarter wave plate (QWP) 1730. The FPR 3D system 1700 may also includean analyzer subsystem 1760 comprising eyewear 1740 having analyzing QWPs1742 and polarizers 1744. The stripe patterned QWP 1730 may be alignedwith LCD pixel stripes (not shown) in the LCD panel 1705 in thehorizontal direction or vertical direction. To compensate for the abovediscussed low contrast and the narrow FOV, a half wave +C-plate 1720 maybe disposed before the stripe patterned QWP 1730 at the display side asshown in FIG. 17.

FIG. 18 is a schematic diagram of another embodiment of a compensatedFPR system 1800, in accordance with the disclosed principles. The FPR 3Dsystem 1800 may include an image source subsystem 1850 comprising an LCDpanel 1805, optically followed by an exit polarizer 1810, and a stripepatterned quarter wave plate (QWP) 1830. The FPR 3D system 1800 may alsoinclude an analyzer subsystem 1860 comprising eyewear 1840 havinganalyzing QWPs 1842 and polarizers 1844. A half wave +C-plate 1820 maybe disposed after the QWPs 1742 on the eyewear 1840 side, in accordancewith the principles disclosed herein for providing compensation.

FIG. 19 is a polar plot of contrast ratio for an FPR system compensatedaccording to the disclosed configuration of a compensated FPR system1700 or 1800. As illustrated, the addition of the +C-plate 1720 or 1820has led to significant improvement in off-angle contrast.

FIG. 20A is a schematic diagram of a passive dual-projectionstereoscopic system 2000, similar to the dual projection passive XL 3Dsystem developed by RealD Inc. of Beverly Hills, Calif., which is alsothe Assignee of the present disclosure. The dual projection system 2000comprises left and right projectors 2010 operable to provide left- andright-eye images, respectively. The dual projection system 2000 furthercomprises passive polarization units 2020 for polarizing the left- andright-eye images to substantially orthogonal polarizations. Thepolarized left- and right-eye images are then projected onto thepolarization preserving screen 2030 for a viewer (not shown) to observe.The viewer may use analyzing eyewear (not shown) to separate the left-and right-eye images based on the orthogonal polarizations of thestereoscopic images. It is to be appreciated that the model 100 in FIG.1 may be used to model the combination of the left projector 2010, theleft polarization unit 2020, and the screen 2030, and the combination ofthe right projector 2010, the right polarization unit 2020, and thescreen 2030. As such, the embodiments of compensation configurationsdisclosed herein may each be incorporated into the system 2000.

FIG. 20B is a schematic diagram showing an exemplary embodiment of acompensation configuration of the present disclosure incorporated intothe system 2000 of FIG. 20A. Specifically, FIG. 20B illustrates close upviews of the passive polarization units 2020 illustrated in FIG. 20A, aswell as the viewer worn eyewear 2060. In the illustrated embodiment, thecompensation configuration may include a +C-plate 2040 disposed at leastin one of the left or right polarization units 2020 to compensate forcrossed quarter wave plates 2050 in the left or right polarization units2020 and the corresponding lens of the eyewear 2060. The use of a+C-plate to compensate for crossed QWPs was described in detail abovewith respect to FIGS. 8A and 8B, and is fully applicable here for thesystem 2000. Further, in an embodiment, the same compensationconfiguration may be incorporated in both the left and rightpolarization units 2020, thereby providing a compensated dual projectionsystem.

While various embodiments in accordance with the principles disclosedherein have been described above, it should be understood that they havebeen presented by way of example only, and not limitation. Thus, thebreadth and scope of this disclosure should not be limited by any of theabove-described exemplary embodiments, but should be defined only inaccordance with any claims and their equivalents issuing from thisdisclosure. Furthermore, the above advantages and features are providedin described embodiments, but shall not limit the application of suchissued claims to processes and structures accomplishing any or all ofthe above advantages.

Additionally, the section headings herein are provided for consistencywith the suggestions under 37 CFR 1.77 or otherwise to provideorganizational cues. These headings shall not limit or characterize theembodiment(s) set out in any claims that may issue from this disclosure.Specifically and by way of example, although the headings refer to a“Technical Field,” the claims should not be limited by the languagechosen under this heading to describe the so-called field. Further, adescription of a technology in the “Background” is not to be construedas an admission that certain technology is prior art to anyembodiment(s) in this disclosure. Neither is the “Summary” to beconsidered as a characterization of the embodiment(s) set forth inissued claims. Furthermore, any reference in this disclosure to“invention” in the singular should not be used to argue that there isonly a single point of novelty in this disclosure. Multiple embodimentsmay be set forth according to the limitations of the multiple claimsissuing from this disclosure, and such claims accordingly define theembodiment(s), and their equivalents, that are protected thereby. In allinstances, the scope of such claims shall be considered on their ownmerits in light of this disclosure, but should not be constrained by theheadings set forth herein.

What is claimed is:
 1. A stereoscopic imaging system, comprising: animage source subsystem operable to output light of first and secondstates of polarization (SOP); an analyzer subsystem operable tosubstantially block light of the first SOP from traveling along a firstpath, and to substantially block light of the second SOP from travelingalong a second path; wherein the image source subsystem comprises afirst optical element operable to cause a first polarization change onlight passing therethrough, and the analyzer subsystem comprises asecond optical element operable to cause a second polarization change onlight passing therethrough; wherein the first and second polarizationchanges, if not compensated, would at least partially cause at least oneof a leakage of light of the first SOP along the first path or a leakageof light of the second SOP along the second path; and wherein the imagesource subsystem or the analyzer subsystem comprises a compensatorconfigured to at least reduce both the first and second polarizationchanges.
 2. The stereoscopic imaging system of claim 1, wherein theimage source subsystem comprises at least one projector, and thecompensator is disposed in the image source subsystem opticallyfollowing the at least one projector.
 3. The stereoscopic imaging systemof claim 1, wherein the first and second polarization changes eachcomprise a geometric rotation, and the compensator comprises a biaxiallystretched retarder operable to substantially correct the geometricrotation.
 4. The stereoscopic imaging system of claim 1, wherein thefirst and second polarization changes each comprise a geometricrotation, and the compensator comprises a +A-plate and a +C-plateoperable to cooperate to substantially correct a combined geometricrotation of the first and second polarization changes.
 5. Thestereoscopic imaging system of claim 1, wherein the first and secondpolarization changes each comprise a −C-plate type retardation, and thecompensator comprises at least one +C-plate operable to substantiallycorrect a combined −C-plate type retardation of the first and secondpolarization changes.
 6. The stereoscopic imaging system of claim 1,wherein the compensator is optimized for performance measurements for anideal viewer centered horizontally with respect to screen center.
 7. Thestereoscopic imaging system of claim 6, wherein the compensator isoptimized for baseline acceptable performance measurements for viewersin extreme locations of a viewing space with respect to the location ofthe ideal viewer.
 8. The stereoscopic imaging system of claim 6, whereinthe compensator is optimized for maximizing performance measurements foras large a population surrounding the ideal viewer as possible.
 9. Thestereoscopic imaging system of claim 1, wherein the image sourcesubsystem comprises a sequentially or spatially modulated LCD paneloperable to output light of the first and second states of polarization.